In the UK, the Ted Wragg Teaching Award for Lifetime Achievement honours his memory, and is given out annually to educators who are considered to have shown excellent devotion to teaching throughout their careers.

In 1978 he returned to Exeter as a Professor where he headed the amalgamation of the Exeter Education department with St Luke's College. While at Exeter he directed numerous research projects on such topics as classroom processes, teaching strategies, curriculum evaluation, appraising competence and incompetence, and performance-related pay.[7][8] He also studied education in numerous countries around the world. Throughout his academic career he would always make time to teach a class of children for one or two days a week so that he would remain in touch with the profession at the 'chalkface'.

He was a frequent broadcaster on radio and television and wrote regularly in newspapers including the Times Educational Supplement[1] and The Guardian. Wragg was an advocate of warmth, humour and humanity in the classroom and defended these ideals with passion against a narrowly utilitarian approach to learning; he was vociferous in opposing attempts to roll back the education changes of the 1960s. He had a ready and sharp wit, which worked well with his savage indignation at politically inspired educational reforms. Although initially his beliefs were reflected by the government of Tony Blair, he later fell out with it and attacked it, nicknaming Ruth Kelly "Ruth Dalek" and "The Duchess of Drivel"; he also coined the nickname 'Tony Zoffis' (Tony's office) for Andrew Adonis, then a member of the Downing Street policy unit but subsequently ennobled and appointed as Parliamentary Under Secretary of State for Education.